Background: Aging is associated with various chronic conditions, such as cognitive and muscle strength decline. Previous studies have analysed the association between physical factors and cognitive decline however, the magnitude and the direction of the association between handgrip strength (HGS) and cognitive decline are not fully understood. Objectives: To analyse the association between HGS and cognitive decline in numeracy, recall and verbal fluency according to sex in a large multicentric population. Methods: A longitudinal study including people aged 50 and over from the Survey of Health, Aging and Retirement in Europe (SHARE) was conducted, involving participants from 28 European countries. Repeated HGS measures from a dynamometer and cognitive scores in numeracy, recall, and verbal fluency were biannually analysed for 4 years. Individuals with Parkinson along the study or dementia diagnosis at baseline were excluded. For the analysis of HGS as a predictor of future cognitive decline, HGS was categorized in quintiles by sex. In men HGS quintiles were Q1 (8-35kg), Q2 (36-41kg), Q3 (42-45kg), Q4 (46-50kg) and Q5 (51-80kg). In women HGS quintiles were Q1 (4-21kg), Q2 (22-25 kg), Q3 (26-28 kg), Q4 (29-32 kg) and Q5 (33-55 kg). First quintile in each sex was used as reference. In the analysis of cognitive performance as a predictor of HGS decline, different cognitive scores were treated in their logarithmical form as a function of HGS continuously. Possible confounding factors were controlled through general estimated equations and adjusted for baseline handgrip strength quintile and time-varying covariates as age, time, education, smoking status, alcohol consumption, physical activity, BMI index, chronical illnesses, Alzheimer disease, depression, functionality scores, and sarcopenia. Results: A total of 8,236 individuals were included, 55.73% were females with a mean age of 67.55 (± 8.4) years, while in males it was of 68.42 (±7.7) years. A significant longitudinal association between HGS and cognitive function in all three domains was found in both sexes, except numeracy in males. The fully adjusted β coefficients CI (95%) for the fifth HGS quintile in numeracy, verbal fluency and recall were 0.041 (0.004-0.082), 0.078 (0.038-0.117) and 0.095 (0.039-0.151) respectively for men and 0.076 (0.039-0.113), 0.094 (0.060-0.0128) and 0.092 (0.047-0.137) respectively for women. On the other hand the greatest cognitive predictor of HGS was verbal fluency in both sexes, β(95%), 0.796 (0.464 to 1.128)kg in men and 0.801 (0.567 to 1.109)kg in women. Conclusion: There is a significant and bidirectional association between HGS and the cognitive performance in men and women over 50 years studied in SHARE.